V_HISTNDIM - generates and/or plots an n-dimensional histogram
Inputs: X(m,d) is the input data: each row is one d-dimensiona data point
B(3,d) specifies the histogram bins.
B(1,:) gives the number of bins in each dmension [default 10]
B(2,:) gives the minimum of the first bin in each dimension [default min(X)]
B(3,:) gives the maximum of the last bin in each dimension [default max(X)]
If B has only one column, the same values are use for al dimensions
If B(1,i)=0 then that dimension will be ignored (and excluded from V)
MODE is a character string containing a combination of the following:
'z' for zero base in the 2D plot [default base = min(V)]
'p' to scale V as probabilities [default actual counts]
'h' to plot a histogam even if output arguments are present
Outputs: V d-dimensional array containing the histogram counts
T d-element cell array. d{i} contains the bin boundary values for
the i'th dimension. The length of d{i} is one more than the number of bins
in that dimension.
Note that if any of B(1,:) are zero then the number of dimensions in V and elements
of T will be correspondingly reduced.
Example: v_histndim(randn(100000,2),[20 -3 3]','pz');0001 function [v,t]=v_histndim(x,b,mode) 0002 %V_HISTNDIM - generates and/or plots an n-dimensional histogram 0003 % 0004 % Inputs: X(m,d) is the input data: each row is one d-dimensiona data point 0005 % B(3,d) specifies the histogram bins. 0006 % B(1,:) gives the number of bins in each dmension [default 10] 0007 % B(2,:) gives the minimum of the first bin in each dimension [default min(X)] 0008 % B(3,:) gives the maximum of the last bin in each dimension [default max(X)] 0009 % If B has only one column, the same values are use for al dimensions 0010 % If B(1,i)=0 then that dimension will be ignored (and excluded from V) 0011 % MODE is a character string containing a combination of the following: 0012 % 'z' for zero base in the 2D plot [default base = min(V)] 0013 % 'p' to scale V as probabilities [default actual counts] 0014 % 'h' to plot a histogam even if output arguments are present 0015 % 0016 % Outputs: V d-dimensional array containing the histogram counts 0017 % T d-element cell array. d{i} contains the bin boundary values for 0018 % the i'th dimension. The length of d{i} is one more than the number of bins 0019 % in that dimension. 0020 % 0021 % Note that if any of B(1,:) are zero then the number of dimensions in V and elements 0022 % of T will be correspondingly reduced. 0023 % 0024 % Example: v_histndim(randn(100000,2),[20 -3 3]','pz'); 0025 0026 % Copyright (C) Mike Brookes 2004 0027 % Version: $Id: v_histndim.m 10865 2018-09-21 17:22:45Z dmb $ 0028 % 0029 % VOICEBOX is a MATLAB toolbox for speech processing. 0030 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0031 % 0032 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0033 % This program is free software; you can redistribute it and/or modify 0034 % it under the terms of the GNU General Public License as published by 0035 % the Free Software Foundation; either version 2 of the License, or 0036 % (at your option) any later version. 0037 % 0038 % This program is distributed in the hope that it will be useful, 0039 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0040 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0041 % GNU General Public License for more details. 0042 % 0043 % You can obtain a copy of the GNU General Public License from 0044 % http://www.gnu.org/copyleft/gpl.html or by writing to 0045 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0046 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0047 0048 [n,d]=size(x); 0049 if nargin<3 0050 mode=' '; 0051 if(nargin<2) 0052 b=repmat(10,1,d); 0053 end 0054 end 0055 0056 if size(b,2)==1 0057 b=repmat(b,1,d); 0058 end 0059 if size(b,1)<3 0060 mi=min(x,[],1); 0061 ma=max(x,[],1); 0062 w=(ma-mi)./(b(1,:)-0.001); % nudge slightly to make sure al points included 0063 b(3,:)=ma+0.0005*w; 0064 b(2,:)=mi-0.0005*w; 0065 end 0066 0067 acd=find(b(1,:)>0); 0068 sv=b(1,acd); 0069 nbt=prod(sv); 0070 t=cell(length(acd),1); 0071 0072 % loop through each dimension 0073 k=1; % indexing factor 0074 ok=repmat(1>0,n,1); 0075 ix=repmat(nbt-sum(cumprod(sv)),n,1); 0076 for i=1:length(acd) 0077 j=acd(i); 0078 bw=b(1,j)/(b(3,j)-b(2,j)); 0079 bi=ceil((x(:,j)-b(2,j))*bw); 0080 ok=ok & (bi>0) & (bi<=b(1,j)); 0081 ix(ok)=ix(ok)+k*bi(ok); 0082 k=k*b(1,j); 0083 t{i}=b(2,j)+(0:b(1,j))/bw; 0084 end 0085 v=full(sparse(ix(ok),1,1,nbt,1)); 0086 if length(sv)>1 0087 v=reshape(v,sv); 0088 end 0089 if any(mode=='p') 0090 v=v/n; 0091 end 0092 0093 if ~nargout | any(mode=='h') 0094 svg=find(sv>1); 0095 if length(svg)==1 0096 j=acd(svg); 0097 bar(b(2,j)+(0.5:sv(svg)-0.5)*(b(3,j)-b(2,j))/b(1,j),v(:)); 0098 elseif length(svg)==2 0099 j=acd(svg(1)); 0100 k=acd(svg(2)); 0101 bj=b(1,j); 0102 bk=b(1,k); 0103 % imagesc(b(2:3,k),b(2:3,j),reshape(v,b(1,j),b(1,k))); 0104 vda=kron(reshape(v,bj,bk),[1 1;1 1]); 0105 if any(mode=='z') 0106 ba=0; 0107 else 0108 ba=min(vda(:)); 0109 end 0110 vda=[repmat(ba,1,2*bk+2);repmat(ba,2*bj,1) vda repmat(ba,2*bj,1);repmat(ba,1,2*bk+2)]; 0111 jda=kron(t{svg(1)},[1 1]); 0112 jda=jda-(jda(3)-jda(2))*0.01*[-0.5 (-1).^(1:2*bj) 0.5]; % nudge slightly to avoid MATLAB plotting bug 0113 kda=kron(t{svg(2)},[1 1]); 0114 kda=kda-(kda(3)-kda(2))*0.01*[-0.5 (-1).^(1:2*bk) 0.5]; 0115 surf(jda,kda,vda'); 0116 ylabel(sprintf('Axis %d',k)); 0117 xlabel(sprintf('Axis %d',j)); 0118 colorbar; 0119 else 0120 fprintf(2,'Error in %s: Cannot plot 3-D histogram\n',mfilename); 0121 end 0122 end